如何识别马约喇纳子：自发轻子数破缺的有效场论
How to Identify a Majoron: Effective Field Theories of Spontaneous Lepton Number Breaking
AI总结：
该研究在含轻子数和Peccei-Quinn对称性的复标量场下重新审视三类跷跷板机制，构建马约喇纳子的有效场论，通过匹配阶分析预言可观测量关系，给出轻子数破缺能标下限，且框架可证伪。
AI中文摘要：
我们在存在带全局$U(1)$对称性（可被识别为轻子数和Peccei-Quinn对称性）的复标量场的情况下，重新审视传统的I型、II型和III型跷跷板机制。对称性破缺后，径向模式变得很重，而角模式表现为类轴子粒子，通常被称为马约喇纳子。我们构造了积分掉重态后得到的有效场论，并分析了两种匹配阶：先去除径向模式再去除跷跷板场，反之亦然。两种过程都得到仅包含标准模型场和马约喇纳子的相同低能拉格朗日量。由于单一真空期望值决定了中介质量、径向模式和每个马约喇纳子耦合，这些模型预测可观测量之间存在关系而非其单独大小，且正是这些关系可被检验。实际上，不可见的希格斯宽度被锁定到希格斯耦合的通用压低，而马约喇纳子-轻子耦合由测量到的轻子混合矩阵的非幺正性确定，两者独立给出对同一轻子数破缺能标的相当下限，量级为1-10 TeV。相比之下，马约喇纳子发射的无中微子双β衰变在这类模型中无敏感性。因此，即使新态远超出实验可达范围，该框架仍是可证伪的。
英文摘要：
We revisit the traditional Type I, II and III Seesaw mechanisms in the presence of a complex scalar field charged under a global $U(1)$ symmetry that can be identified with lepton number and the Peccei-Quinn symmetry. After symmetry breaking, the radial mode becomes heavy while the angular mode appears as an axion-like particle, traditionally dubbed the Majoron. We construct the effective field theory obtained after integrating out the heavy states and analyse two matching orders: first removing the radial mode and then the Seesaw fields, and vice versa. Both procedures yield the same low-energy Lagrangian containing only Standard Model fields and the Majoron. Because a single vacuum expectation value fixes the mediator masses, the radial mode and every Majoron coupling, these models predict relations among observables rather than their individual size, and it is these relations that are testable. Indeed, the invisible Higgs width is locked to the universal suppression of the Higgs couplings, while the Majoron-lepton coupling is fixed by the measured non-unitarity of the leptonic mixing matrix, and the two independently give comparable lower bounds on the same lepton-number breaking scale, of order $1$-$10$ TeV. Neutrinoless double beta decay with Majoron emission, by contrast, has no sensitivity in this class of models. The framework is thus falsifiable even when the new states lie far beyond experimental reach.
